Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach

Vladica S. Stojanović, Hassan S. Bakouch, Eugen Ljajko and Najla Qarmalah ()
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Vladica S. Stojanović: Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11060 Belgrade, Serbia
Hassan S. Bakouch: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Eugen Ljajko: Department of Mathematics, Faculty of Sciences & Mathematics, University of Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia
Najla Qarmalah: Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia

Mathematics, 2023, vol. 11, issue 8, 1-25

Abstract: Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probability-generating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.

Keywords: time series; zero-and-one inflation; probability generating functions; parameter estimation; simulation; COVID-19; application (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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